Answer:
value of w is 25...... .....
It's be a line that crosses the y-axis at (0,7) and has a slope of -3 or -3/1.
By "which is an identity" they just mean "which trigonometric equation is true?"
What you have to do is take one of these and sort it out to an identity you know is true, or...
*FYI: You can always test identites like this:
Use the short angle of a 3-4-5 triangle, which would have these trig ratios:
sinx = 3/5 cscx = 5/3
cosx = 4/5 secx = 5/4
tanx = 4/3 cotx = 3/4
Then just plug them in and see if it works. If it doesn't, it can't be an identity!
Let's start with c, just because it seems obvious.
The Pythagorean identity states that sin²x + cos²x = 1, so this same statement with a minus is obviously not true.
Next would be d. csc²x + cot²x = 1 is not true because of a similar Pythagorean identity 1 + cot²x = csc²x. (if you need help remembering these identites, do yourslef a favor and search up the Magic Hexagon.)
Next is b. Here we have (cscx + cotx)² = 1. Let's take the square root of each side...cscx + cotx = 1. Now you should be able to see why this can't work as a Pythagorean Identity. There's always that test we can do for verification...5/3 + 3/4 ≠ 1, nor is (5/3 + 3/4)².
By process of elimination, a must be true. You can test w/ our example ratios:
sin²xsec²x+1 = tan²xcsc²x
(3/5)²(5/4)²+1 = (4/5)²(5/3)²
(9/25)(25/16)+1 = (16/25)(25/9)
(225/400)+1 = (400/225)
(9/16)+1 = (16/9)
(81/144)+1 = (256/144)
(81/144)+(144/144) = (256/144)
(256/144) = (256/144)
First you make -1 and 3/4 have a common denominator. 1 has a fraction of 1/1 so times four it is 4/4. Then you add on both sides in order to isolate x and you get 3/10x = 7/4.
Then you isolate x by multyiplying the reciprocal of 3/10 on both sides, 10/3.
3/10 and 10/3 cancel out and you get an answer of x = 70/4.
You could then simplify it to get 35/6 by finding a greasted common multiple of 12 and 70 which is 2 and dividing both by 2 to get a simpilier answer.
So the answer is x = 35/6
Answer:
48 minutes.
Step-by-step explanation:
Number of dishes rinsed by Juan in <em>1</em><em> </em><em>m</em><em>i</em><em>n</em><em>u</em><em>t</em><em>e</em><em> </em>
= 480/80
= 6
Number of dishes rinsed by Kevin in <em>1</em><em> </em><em>m</em><em>i</em><em>n</em><em>u</em><em>t</em><em>e</em>
= 480/120
= 4
Number of dishes rinsed by Juan and Kevin in <em>1</em><em> </em><em>m</em><em>i</em><em>n</em><em>u</em><em>t</em><em>e</em>
= 6 + 4
= 10
Hence, time taken by Juan and Kevin to rinse the dishes
= 480/10
= <u>4</u><u>8</u><u> </u><u>m</u><u>i</u><u>n</u><u>u</u><u>t</u><u>e</u><u>s</u>.
Hence It will take <u>4</u><u>8</u><u> </u><u>m</u><u>i</u><u>n</u><u>u</u><u>t</u><u>e</u><u>s</u> for them to rinse the dishes.
